To get [itex]g_1[/itex], they simply added x to both sides of [itex]x^3- x- 5= 0[/itex] to get [itex]x^3- 5= x[/itex].

To get [itex]g_2[/itex], they added x+ 5 to both sides to get [itex]x^3= x+ 5[/itex] and took the cube root of both sides.

To get [itex]g_3[/itex], they subtracted 5 from both sides to get [itex]x^3- x= 5[/itex], then factored, [itex]x(x^2- 1)= 5[/itex] and, finally, divided both sides by [itex]x^2- 1[/itex] to get [itex]x= 5/(x^2- 1)[/itex].